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mentally,' lie told a young friend, *it is a proof that the problem
is mathematically impregnable.'
Remembering his own struggles to get an education and his
mother's sacrifices, Kummer was not only a father to his stu-
dents but something of a brother to their parents. Thousands of
grateful young men who had been helped on their way by
Kummer at the University of Berlin or the War College
remembered him all their lives as a great teacher and a great
friend. Once a needy young mathematician about to come up
for his doctor's examination was stricken with smallpox and
had to return to his home in Posen near the Russian border. No
word came from him, but it was known that he was desperately
poor. When Hummer heard that the young man was probably
unable to afford proper care, he sought out a friend of the
student, gave him the requisite money and sent him off to Posen
to see that what was necessary was done. In his teaching
Kuminer was famous for his homely similes and philosophical
asides. Thus, to drive home the importance of a particular
factor in a certain expression, he observed that 4If you neglect
this factor you will be like a man who in eating a plum swallows
the stone and spits out the pulp.'
The last nine years of Kummer s life were spent in complete
retirement. 'Nothing will be found in my posthumous papers,*
he said, thinking of the mass of work which Gauss left to be
edited after his death* Surrounded by his family (nine children
survived him), Kummer gave up mathematics for good when
he retired, and except for occasional trips to the scenes of his
boyhood lived hi the strictest seclusion. He died after a short
attack of influenza on 14 May 1893, aged eighty-three.
Rummer's successor in arithmetic was Julius Wilnelm
Richard Dedekmd (he dropped the first two names when he
grew up), one of the greatest mathematicians and one of the
most original Germany - or any other country - has produced.
Like Kummer, Dedekind had a long life (6 October 1831-12
February 1916), and he remained mathematically active to
within a short time of his death. When he died in 1918 Dede-
kind had been a mathematical classic for well over a generation.
As Edmund Landau (himself a friend and follower of Dedefcind